Relations and Functions (Class 12)

The function f:(- , ) (- ,1), defined by f(x)= 2x-2-x2x+2-x is :

1. One-one but not onto
2. Onto but not one-one
3. Both one-one and onto
4. Neither one-one nor onto

Number of functions f:\1,2, ,100\ \0,1\, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to .

Let R=\(1,2),(2,3),(3,3)\ be a relation defined on the set \1,2,3,4\. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

1. 9
2. 8
3. 7
4. 10

Let X=R . Define a relation R on X as : (a1,b1)R(a2,b2) b1=b2 In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are true
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are false
4. Statement I is false but Statement II is true

Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y . Then n=1100 ef(n) is equal to :

1. 2406
2. 5220
3. 2525
4. 2384

The number of non-empty equivalence relations on the set \1,2,3\ is :

1. 7
2. 4
3. 5
4. 6

Let A=\1,2,3,4\ and B=\1,4,9,16\. Then the number of many-one functions f:A B such that 1 f(A) is equal to :

1. 151
2. 139
3. 163
4. 127

Let A=\1,2,3\. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .